To summarize, quantum Darwinism clarifies the role of the proliferation
of information in the quantum-to-classical transition. Here, I examined
the quantity introduced by Touil et al. [1]},
\(\chi \left(\mathcal {S}:\check{\mathcal {F}}\right)\) , where an (optimal) measurement
is made on the fragment, reminiscent of the quantum Chernoff bound.
It provides an appealing approach to finding the redundancy of information,
as it is an accessibility bound that becomes the accessible information
in the limit of good decoherence. For the special case of a pure \(\mathcal {S}\mathcal {E}\) 
state, the accessible information is directly related to the optimal
error probability for distinguishing conditional states on the environment
(i.e., hypothesis testing or inference), of which an exact expression
(including the prefactor) can be computed. Moreover, this connection
immediately generalizes the result to any pure, \(D=2\)  model (spin
environments, qudit environments, photon environments, etc.) and
to inhomogeneous environments (including ones with self-Hamiltonians,
as in Eq. (REF )). That decay, as expected, has the same
exponent as the QCB, as the QCB promises (and only promises) to yield
the right asymptotic decay, not the prefactor. Asymptotic analysis
provides a non-empirical way to show that all quantities give the
same redundancy—due to the same exponent—to
leading order (and that corrections are small) and makes universality
of the plateau approach manifest. Since the QCB applies more generally,
its universal bound should further help shed light on future results
that yield exact entropic quantities or alternative bounds. Its importance—the
QCB's importance—goes beyond this, though, as it provides
a single shot, finite \(\mathcal {F}\)  framework for understanding how we observers
learn in a quantum Universe.
